Numerical integration of functions with boundary singularities
TLDR
In this paper, the authors deal with the problem of constructing efficient rules for the numerical evaluation of integrals of functions which are very smooth everywhere in the domain of integration, except at the boundaries where they possess mild singularities.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1999-11-30 and is currently open access. It has received 71 citations till now. The article focuses on the topics: Singular integral & Order of integration (calculus).read more
Citations
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Journal ArticleDOI
Generalized Duffy transformation for integrating vertex singularities
S. E. Mousavi,N. Sukumar +1 more
TL;DR: In this paper, the authors generalize the Duffy trans-formation to power singularities of the form p(x)/r α, where p is a trivariate polynomial and α> 0 is the strength of the singularity.
Journal ArticleDOI
An energy approach to space-time Galerkin BEM for wave propagation problems
TL;DR: In this article, the authors considered Dirichlet or Neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential, and showed unconditional stability of the space-time Galerkin boundary element method applied to the energetic weak problem.
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On the computation of nearly singular integrals in 3D BEM collocation
TL;DR: In this article, the authors proposed an efficient strategy to compute nearly singular integrals over planar triangles in R3 arising in boundary element method collocation, which is based on a proper use of various non-linear transformations, which smooth or move away or quite eliminate all the singularities close to the domain of integration.
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Analytical integrations of hypersingular kernel in 3D BEM problems
TL;DR: In this paper, the analytical integration of the hypersingular kernel in potential problems is presented for 3D symmetric Galerkin boundary element method, adopting linear shape functions, inner integrations are performed both for the finite part of Hadamard and for Lebesgue integrals, working in a local coordinate system.
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A note on true desingularisation of boundary integral methods for three-dimensional potential problems
TL;DR: In this paper, a desingularized boundary element formulation for the three-dimensional potential problem is presented, which is based on integral identities for the fundamental solution and has the advantage that the singular terms on both influence matrices can be directly calculated by replacing it with a special summation of the other off-diagonal elements.
References
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Journal ArticleDOI
Methods of Numerical Integration.
Journal ArticleDOI
Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
TL;DR: In this article, a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex.
Journal ArticleDOI
A Nyström method for boundary integral equations in domains with corners
TL;DR: In this article, a convergence and error analysis for a Nystrom method on a graded mesh for the numerical solution of boundary integral equations for the harmonic Dirichlet problem in plane domains with corners is given.
Book ChapterDOI
A New Variable Transformation for Numerical Integration
TL;DR: This paper proposes a new transformation, denoted the sin m -transformation, that is neither polynomial nor exponential, but trigonometric, in nature, and indicates that transformations in S m can be more advantageous than knownPolynomial transformations, and have less underflow and overflow problems than exponential ones.
OtherDOI
A survey of numerical cubature over triangles
James N. Lyness,Ronald Cools +1 more
TL;DR: A survey of numerical cubature over triangles can be found in this paper, with emphasis on the full corner singularity of the triangle and on the use of polynomial moment fitting.